Potential Difference in a van der graaff generator

[JNBirDy]

Hi, this problem is from 'Electromagnetism' by Grant & Phillips and it states,

Homework Statement

'http://i1129.photobucket.com/albums/m505/physicsbird1/126fig.png" shows a cross-section of the cylindrical high-voltage terminal of a van der Graaff generator, surrounded by an 'intershield' and a pressure vessel, both of which are also cylindrical. The gas in the pressure vessel breaks down in electric fields greater than 1.6 x 10^{7} volts/m. If the radii of the terminal, intershield and pressure vessel are 1.5 m, 2.5 m and 4 m respectively, what is the highest potential difference that can be maintained between the terminal and the pressure vessel?'

The answers given in the back of the book: '31.1 MV. When the terminal is at this voltage the intershield must be at 18.8MV to prevent breakdown.'

Homework Equations

d∅ = -E\bulletdr

E = q/4πε₀r^{2}

The Attempt at a Solution

1.6x10^{7} = q/4πε₀(2.5)^{2}

1.00x10^{8} = q/4πε₀ (Let q/4πε₀ = A)

A = 1.00x10^{8}


∅_{B} - ∅_{A} = -1.00x10^{8}\int^{4}_{1.5}(1/r^{2})

= -1.00x10^{8}[-1/r]^{4}_{1.5}<br /> <br /> = -1.00x10^{8} [-1/4 + 1/1.5]<br /> <br /> = -4.17x10^{7}<br /> <br /> So... can anybody tell me where I&#039;ve went wrong?

 

[Spinnor]

Londonfish is doing the same problem, are you in the same class? See,

https://www.physicsforums.com/showthread.php?p=3541803#post3541803

 

[Spinnor]

You wrote, "E = q/4πε₀r^2"

E goes as 1/r ?